Even though Grover's algorithm is optimal as a quantum searching algorithm[1]}, such maximal creation and complete annihilation of entanglement do not occur for large \(N\) .
For example, let us consider \(N = 8\)  case. If \(\vert \psi _G \rangle  = \vert 7 \rangle  = \vert 111 \rangle \) , Grover's algorithm changes the quantum state as
\(&&\vert \psi _1 \rangle  = U_{\mbox{oracle}} \vert s \rangle  = \frac{1}{2 \sqrt{2}} \left( \vert 0 \rangle  + \vert 1 \rangle  + \vert 2 \rangle  + \vert 3 \rangle  + \vert 4 \rangle  + \vert 5 \rangle  + \vert 6 \rangle  - \vert 7 \rangle  \right) \\ \nonumber &&\vert \psi _2 \rangle  = U_{\mbox{diffuser}} \vert \psi _1 \rangle  = \frac{1}{4 \sqrt{2}} \left( \vert 0 \rangle  + \vert 1 \rangle  + \vert 2 \rangle  + \vert 3 \rangle  + \vert 4 \rangle  + \vert 5 \rangle  + \vert 6 \rangle  + 5 \vert 7 \rangle  \right) \\ \nonumber &&\vert \psi _3 \rangle  = U_{\mbox{oracle}} \vert \psi _2 \rangle  = \frac{1}{4 \sqrt{2}} \left( \vert 0 \rangle  + \vert 1 \rangle  + \vert 2 \rangle  + \vert 3 \rangle  + \vert 4 \rangle  + \vert 5 \rangle  + \vert 6 \rangle  - 5 \vert 7 \rangle  \right) \\ \nonumber &&\vert \psi _4 \rangle  = U_{\mbox{diffuser}} \vert \psi _3 \rangle  = - \frac{1}{8 \sqrt{2}} \left( \vert 0 \rangle  + \vert 1 \rangle  + \vert 2 \rangle  + \vert 3 \rangle  + \vert 4 \rangle  + \vert 5 \rangle  + \vert 6 \rangle  - 11 \vert 7 \rangle  \right).\) 
